背景

什么是 NumPy 呢？

NumPy 这个词来源于两个单词 – Numerical和Python。其是一个功能强大的 Python 库，可以帮助程序员轻松地进行数值计算，通常应用于以下场景：

• 执行各种数学任务，如：数值积分、微分、内插、外推等。因此，当涉及到数学任务时，它形成了一种基于 Python 的 MATLAB 的快速替代。
• 计算机中的图像表示为多维数字数组。NumPy 提供了一些优秀的库函数来快速处理图像。例如，镜像图像、按特定角度旋转图像等。
• 在编写机器学习算法时，需要对矩阵进行各种数值计算。如：矩阵乘法、求逆、换位、加法等。NumPy 数组用于存储训练数据和机器学习模型的参数。

数组操作

更改形状

在对数组进行操作时，为了满足格式和计算的要求通常会改变其形状。

• numpy.ndarray.shape表示数组的维度，返回一个元组，这个元组的长度就是维度的数目，即 ndim 属性(秩)。

【例】通过修改 shap 属性来改变数组的形状。

import numpy as npx = np.array([1, 2, 9, 4, 5, 6, 7, 8])
print(x.shape)  # (8,)
x.shape = [2, 4]
print(x)
# [[1 2 9 4]
#  [5 6 7 8]]

• numpy.ndarray.flat 将数组转换为一维的迭代器，可以用for访问数组每一个元素。

【例】

import numpy as npx = np.array([[11, 12, 13, 14, 15],[16, 17, 18, 19, 20],[21, 22, 23, 24, 25],[26, 27, 28, 29, 30],[31, 32, 33, 34, 35]])
y = x.flat
print(y)
# <numpy.flatiter object at 0x0000020F9BA10C60>
for i in y:print(i, end=' ')
# 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35y[3] = 0
print(end='\n')
print(x)
# [[11 12 13  0 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]

• numpy.ndarray.flatten([order='C']) 将数组的++副本++转换为一维数组，并返回。
  • order = {'C', 'F'}，‘C’：C-style，行序优先、‘F’：Fortran-style，列序优先。

【例】flatten()函数返回的是拷贝。

import numpy as npx = np.array([[11, 12, 13, 14, 15],[16, 17, 18, 19, 20],[21, 22, 23, 24, 25],[26, 27, 28, 29, 30],[31, 32, 33, 34, 35]])
y = x.flatten()
print(y)
# [11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
#  35]y[3] = 0
print(x)
# [[11 12 13 14 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]x = np.array([[11, 12, 13, 14, 15],[16, 17, 18, 19, 20],[21, 22, 23, 24, 25],[26, 27, 28, 29, 30],[31, 32, 33, 34, 35]])y = x.flatten(order='F')
print(y)
# [11 16 21 26 31 12 17 22 27 32 13 18 23 28 33 14 19 24 29 34 15 20 25 30
#  35]y[3] = 0
print(x)
# [[11 12 13 14 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]

• numpy.reshape(a, newshape[, order='C'])在不更改数据的情况下为数组赋予新的形状。

【例】

import numpy as npx = np.arange(0, 12)
y = np.reshape(x, [3, 4])
print(y, y.dtype)
# [[ 0  1  2  3]
#  [ 4  5  6  7]
#  [ 8  9 10 11]] int32y[0, 1] = 10
print(x)
# [ 0 10  2  3  4  5  6  7  8  9 10 11]

【例】reshape()函数当参数newshape = -1时表示将数组降为一维。

import numpy as npx = np.random.randint(12, size=[2, 2, 3])
print(x)
# [[[11  9  1]
#   [ 1 10  3]]
# 
#  [[ 0  6  1]
#   [ 4 11  3]]]
y = np.reshape(x, -1)
print(y)
# [11  9  1  1 10  3  0  6  1  4 11  3]

• numpy.ravel(a, order='C')Return a contiguous flattened array.

【例】ravel()返回的是视图。

import numpy as npx = np.array([[11, 12, 13, 14, 15],[16, 17, 18, 19, 20],[21, 22, 23, 24, 25],[26, 27, 28, 29, 30],[31, 32, 33, 34, 35]])
y = np.ravel(x)
print(y)
# [11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
#  35]y[3] = 0
print(x)
# [[11 12 13  0 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]x = np.array([[11, 12, 13, 14, 15],[16, 17, 18, 19, 20],[21, 22, 23, 24, 25],[26, 27, 28, 29, 30],[31, 32, 33, 34, 35]])y = np.ravel(x, order='F')
print(y)
# [11 16 21 26 31 12 17 22 27 32 13 18 23 28 33 14 19 24 29 34 15 20 25 30
#  35]y[3] = 0
print(x)
# [[11 12 13 14 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]

数组转置

• numpy.transpose(a, axes=None) Permute the dimensions of an array.
• numpy.ndarray.T Same as self.transpose(), except that self is returned if self.ndim < 2.

【例】

import numpy as npx = np.random.rand(5, 5) * 10
x = np.around(x, 2)
print(x)
# [[6.74 8.46 6.74 5.45 1.25]
#  [3.54 3.49 8.62 1.94 9.92]
#  [5.03 7.22 1.6  8.7  0.43]
#  [7.5  7.31 5.69 9.67 7.65]
#  [1.8  9.52 2.78 5.87 4.14]]
y = x.T
print(y)
# [[6.74 3.54 5.03 7.5  1.8 ]
#  [8.46 3.49 7.22 7.31 9.52]
#  [6.74 8.62 1.6  5.69 2.78]
#  [5.45 1.94 8.7  9.67 5.87]
#  [1.25 9.92 0.43 7.65 4.14]]
y = np.transpose(x)
print(y)
# [[6.74 3.54 5.03 7.5  1.8 ]
#  [8.46 3.49 7.22 7.31 9.52]
#  [6.74 8.62 1.6  5.69 2.78]
#  [5.45 1.94 8.7  9.67 5.87]
#  [1.25 9.92 0.43 7.65 4.14]]

更改维度

当创建一个数组之后，还可以给它增加一个维度，这在矩阵计算中经常会用到。

• numpy.newaxis = None None的别名，对索引数组很有用。

【例】很多工具包在进行计算时都会先判断输入数据的维度是否满足要求，如果输入数据达不到指定的维度时，可以使用newaxis参数来增加一个维度。

import numpy as npx = np.array([1, 2, 9, 4, 5, 6, 7, 8])
print(x.shape)  # (8,)
print(x)  # [1 2 9 4 5 6 7 8]y = x[np.newaxis, :]
print(y.shape)  # (1, 8)
print(y)  # [[1 2 9 4 5 6 7 8]]y = x[:, np.newaxis]
print(y.shape)  # (8, 1)
print(y)
# [[1]
#  [2]
#  [9]
#  [4]
#  [5]
#  [6]
#  [7]
#  [8]]

• numpy.squeeze(a, axis=None) 从数组的形状中删除单维度条目，即把shape中为1的维度去掉。
  • a表示输入的数组；
  • axis用于指定需要删除的维度，但是指定的维度必须为单维度，否则将会报错；

在机器学习和深度学习中，通常算法的结果是可以表示向量的数组（即包含两对或以上的方括号形式[[]]），如果直接利用这个数组进行画图可能显示界面为空（见后面的示例）。我们可以利用squeeze()函数将表示向量的数组转换为秩为1的数组，这样利用 matplotlib 库函数画图时，就可以正常的显示结果了。

【例】

import numpy as npx = np.arange(10)
print(x.shape)  # (10,)
x = x[np.newaxis, :]
print(x.shape)  # (1, 10)
y = np.squeeze(x)
print(y.shape)  # (10,)

【例】

import numpy as npx = np.array([[[0], [1], [2]]])
print(x.shape)  # (1, 3, 1)
print(x)
# [[[0]
#   [1]
#   [2]]]y = np.squeeze(x)
print(y.shape)  # (3,)
print(y)  # [0 1 2]y = np.squeeze(x, axis=0)
print(y.shape)  # (3, 1)
print(y)
# [[0]
#  [1]
#  [2]]y = np.squeeze(x, axis=2)
print(y.shape)  # (1, 3)
print(y)  # [[0 1 2]]y = np.squeeze(x, axis=1)
# ValueError: cannot select an axis to squeeze out which has size not equal to one

【例】

import numpy as np
import matplotlib.pyplot as pltx = np.array([[1, 4, 9, 16, 25]])
print(x.shape)  # (1, 5)
plt.plot(x)
plt.show()

【例】

import numpy as np
import matplotlib.pyplot as pltx = np.array([[1, 4, 9, 16, 25]])
x = np.squeeze(x)
print(x.shape)  # (5, )
plt.plot(x)
plt.show()

组合数组

如果要将两份数据组合到一起，就需要拼接操作。

• numpy.concatenate((a1, a2, ...), axis=0, out=None) Join a sequence of arrays along an existing axis.

【例】连接沿现有轴的数组序列（原来x，y都是一维的，拼接后的结果也是一维的）。

import numpy as npx = np.array([1, 2, 3])
y = np.array([7, 8, 9])
z = np.concatenate([x, y])
print(z)
# [1 2 3 7 8 9]z = np.concatenate([x, y], axis=0)
print(z)
# [1 2 3 7 8 9]

【例】原来x，y都是二维的，拼接后的结果也是二维的。

import numpy as npx = np.array([1, 2, 3]).reshape(1, 3)
y = np.array([7, 8, 9]).reshape(1, 3)
z = np.concatenate([x, y])
print(z)
# [[ 1  2  3]
#  [ 7  8  9]]
z = np.concatenate([x, y], axis=0)
print(z)
# [[ 1  2  3]
#  [ 7  8  9]]
z = np.concatenate([x, y], axis=1)
print(z)
# [[ 1  2  3  7  8  9]]

【例】x，y在原来的维度上进行拼接。

import numpy as npx = np.array([[1, 2, 3], [4, 5, 6]])
y = np.array([[7, 8, 9], [10, 11, 12]])
z = np.concatenate([x, y])
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]
z = np.concatenate([x, y], axis=0)
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]
z = np.concatenate([x, y], axis=1)
print(z)
# [[ 1  2  3  7  8  9]
#  [ 4  5  6 10 11 12]]

• numpy.stack(arrays, axis=0, out=None)Join a sequence of arrays along a new axis.

【例】沿着新的轴加入一系列数组（stack为增加维度的拼接）。

import numpy as npx = np.array([1, 2, 3])
y = np.array([7, 8, 9])
z = np.stack([x, y])
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]z = np.stack([x, y], axis=1)
print(z.shape)  # (3, 2)
print(z)
# [[1 7]
#  [2 8]
#  [3 9]]

【例】

import numpy as npx = np.array([1, 2, 3]).reshape(1, 3)
y = np.array([7, 8, 9]).reshape(1, 3)
z = np.stack([x, y])
print(z.shape)  # (2, 1, 3)
print(z)
# [[[1 2 3]]
#
#  [[7 8 9]]]z = np.stack([x, y], axis=1)
print(z.shape)  # (1, 2, 3)
print(z)
# [[[1 2 3]
#   [7 8 9]]]z = np.stack([x, y], axis=2)
print(z.shape)  # (1, 3, 2)
print(z)
# [[[1 7]
#   [2 8]
#   [3 9]]]

【例】

import numpy as npx = np.array([[1, 2, 3], [4, 5, 6]])
y = np.array([[7, 8, 9], [10, 11, 12]])
z = np.stack([x, y])
print(z.shape)  # (2, 2, 3)
print(z)
# [[[ 1  2  3]
#   [ 4  5  6]]
# 
#  [[ 7  8  9]
#   [10 11 12]]]z = np.stack([x, y], axis=1)
print(z.shape)  # (2, 2, 3)
print(z)
# [[[ 1  2  3]
#   [ 7  8  9]]
# 
#  [[ 4  5  6]
#   [10 11 12]]]z = np.stack([x, y], axis=2)
print(z.shape)  # (2, 3, 2)
print(z)
# [[[ 1  7]
#   [ 2  8]
#   [ 3  9]]
# 
#  [[ 4 10]
#   [ 5 11]
#   [ 6 12]]]

• numpy.vstack(tup)Stack arrays in sequence vertically (row wise).
• numpy.hstack(tup)Stack arrays in sequence horizontally (column wise).

【例】一维的情况。

import numpy as npx = np.array([1, 2, 3])
y = np.array([7, 8, 9])
z = np.vstack((x, y))
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]z = np.stack([x, y])
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]z = np.hstack((x, y))
print(z.shape)  # (6,)
print(z)
# [1  2  3  7  8  9]z = np.concatenate((x, y))
print(z.shape)  # (6,)
print(z)  # [1 2 3 7 8 9]

【例】二维的情况。

import numpy as npx = np.array([1, 2, 3]).reshape(1, 3)
y = np.array([7, 8, 9]).reshape(1, 3)
z = np.vstack((x, y))
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]z = np.concatenate((x, y), axis=0)
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]z = np.hstack((x, y))
print(z.shape)  # (1, 6)
print(z)
# [[ 1  2  3  7  8  9]]z = np.concatenate((x, y), axis=1)
print(z.shape)  # (1, 6)
print(z)
# [[1 2 3 7 8 9]]

【例】二维的情况。

import numpy as npx = np.array([[1, 2, 3], [4, 5, 6]])
y = np.array([[7, 8, 9], [10, 11, 12]])
z = np.vstack((x, y))
print(z.shape)  # (4, 3)
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]z = np.concatenate((x, y), axis=0)
print(z.shape)  # (4, 3)
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]z = np.hstack((x, y))
print(z.shape)  # (2, 6)
print(z)
# [[ 1  2  3  7  8  9]
#  [ 4  5  6 10 11 12]]z = np.concatenate((x, y), axis=1)
print(z.shape)  # (2, 6)
print(z)
# [[ 1  2  3  7  8  9]
#  [ 4  5  6 10 11 12]]

hstack(),vstack()分别表示水平和竖直的拼接方式。在数据维度等于1时，比较特殊。而当维度大于或等于2时，它们的作用相当于concatenate，用于在已有轴上进行操作。

拆分数组

• numpy.split(ary, indices_or_sections, axis=0) Split an array into multiple sub-arrays as views into ary.

【例】拆分数组。

import numpy as npx = np.array([[11, 12, 13, 14],[16, 17, 18, 19],[21, 22, 23, 24]])
y = np.split(x, [1, 3])
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]]), array([], shape=(0, 4), dtype=int32)]y = np.split(x, [1, 3], axis=1)
print(y)
# [array([[11],
#        [16],
#        [21]]), array([[12, 13],
#        [17, 18],
#        [22, 23]]), array([[14],
#        [19],
#        [24]])]

• numpy.vsplit(ary, indices_or_sections) Split an array into multiple sub-arrays vertically (row-wise).

【例】垂直切分是把数组按照高度切分

import numpy as npx = np.array([[11, 12, 13, 14],[16, 17, 18, 19],[21, 22, 23, 24]])
y = np.vsplit(x, 3)
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19]]), array([[21, 22, 23, 24]])]y = np.split(x, 3)
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19]]), array([[21, 22, 23, 24]])]y = np.vsplit(x, [1])
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]])]y = np.split(x, [1])
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]])]y = np.vsplit(x, [1, 3])
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]]), array([], shape=(0, 4), dtype=int32)]
y = np.split(x, [1, 3], axis=0)
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]]), array([], shape=(0, 4), dtype=int32)]

• numpy.hsplit(ary, indices_or_sections) Split an array into multiple sub-arrays horizontally (column-wise).

【例】水平切分是把数组按照宽度切分。

import numpy as npx = np.array([[11, 12, 13, 14],[16, 17, 18, 19],[21, 22, 23, 24]])
y = np.hsplit(x, 2)
print(y)
# [array([[11, 12],
#        [16, 17],
#        [21, 22]]), array([[13, 14],
#        [18, 19],
#        [23, 24]])]y = np.split(x, 2, axis=1)
print(y)
# [array([[11, 12],
#        [16, 17],
#        [21, 22]]), array([[13, 14],
#        [18, 19],
#        [23, 24]])]y = np.hsplit(x, [3])
print(y)
# [array([[11, 12, 13],
#        [16, 17, 18],
#        [21, 22, 23]]), array([[14],
#        [19],
#        [24]])]y = np.split(x, [3], axis=1)
print(y)
# [array([[11, 12, 13],
#        [16, 17, 18],
#        [21, 22, 23]]), array([[14],
#        [19],
#        [24]])]y = np.hsplit(x, [1, 3])
print(y)
# [array([[11],
#        [16],
#        [21]]), array([[12, 13],
#        [17, 18],
#        [22, 23]]), array([[14],
#        [19],
#        [24]])]y = np.split(x, [1, 3], axis=1)
print(y)
# [array([[11],
#        [16],
#        [21]]), array([[12, 13],
#        [17, 18],
#        [22, 23]]), array([[14],
#        [19],
#        [24]])]

平铺数组

• numpy.tile(A, reps) Construct an array by repeating A the number of times given by reps.

tile是瓷砖的意思，顾名思义，这个函数就是把数组像瓷砖一样铺展开来。

【例】将原矩阵横向、纵向地复制。

import numpy as npx = np.array([[1, 2], [3, 4]])
print(x)
# [[1 2]
#  [3 4]]y = np.tile(x, (1, 3))
print(y)
# [[1 2 1 2 1 2]
#  [3 4 3 4 3 4]]y = np.tile(x, (3, 1))
print(y)
# [[1 2]
#  [3 4]
#  [1 2]
#  [3 4]
#  [1 2]
#  [3 4]]y = np.tile(x, (3, 3))
print(y)
# [[1 2 1 2 1 2]
#  [3 4 3 4 3 4]
#  [1 2 1 2 1 2]
#  [3 4 3 4 3 4]
#  [1 2 1 2 1 2]
#  [3 4 3 4 3 4]]

• numpy.repeat(a, repeats, axis=None) Repeat elements of an array.
  • axis=0，沿着y轴复制，实际上增加了行数。
  • axis=1，沿着x轴复制，实际上增加了列数。
  • repeats，可以为一个数，也可以为一个矩阵。
  • axis=None时就会flatten当前矩阵，实际上就是变成了一个行向量。

【例】重复数组的元素。

import numpy as npx = np.repeat(3, 4)
print(x)  # [3 3 3 3]x = np.array([[1, 2], [3, 4]])
y = np.repeat(x, 2)
print(y)
# [1 1 2 2 3 3 4 4]y = np.repeat(x, 2, axis=0)
print(y)
# [[1 2]
#  [1 2]
#  [3 4]
#  [3 4]]y = np.repeat(x, 2, axis=1)
print(y)
# [[1 1 2 2]
#  [3 3 4 4]]y = np.repeat(x, [2, 3], axis=0)
print(y)
# [[1 2]
#  [1 2]
#  [3 4]
#  [3 4]
#  [3 4]]y = np.repeat(x, [2, 3], axis=1)
print(y)
# [[1 1 2 2 2]
#  [3 3 4 4 4]]

参考文献

• https://blog.csdn.net/csdn15698845876/article/details/73380803

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我是 终身学习者“老马”，一个长期践行“结伴式学习”理念的 中年大叔。

我崇尚分享，渴望成长，于2010年创立了“LSGO软件技术团队”，并加入了国内著名的开源组织“Datawhale”，也是“Dre@mtech”、“智能机器人研究中心”和“大数据与哲学社会科学实验室”的一员。

愿我们一起学习，一起进步，相互陪伴，共同成长。

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